Pore entrance effects on the electrical potential distribution in charged porous membranes and ion channels

Models for the electrical potential distribution in the interfacial region between a fixed charge membrane and an electrolyte solution have traditionally employed the Donnan equilibrium formalism that assumes discontinuous changes in concentrations and electric potential. In the case of the charged capillary membrane model, we propose to check rigorously the validity of this approach by solving the linearized Poisson–Boltzmann equation for the diffuse electrical double layer at the membrane|solution interface. The comparison of the resulting axial distribution for the electric potential with the Donnan potential drop shows that the discontinuous approach is only valid for membrane thicknesses much greater than the Debye length of the problem.